Question

8 power x-1=2 power x+3

Answer 1

Answer:

3

Step-by-step explanation:

8^x-1=2^x+3

(2)^3x-3=2^x+3

power only

3x-3=x+3

3x-x=3+3

2x=6

x=6/2x=3

Answer 2

Answer:

$\large{\underline{\boxed{\sf x = 3}}}$

Step-by-step explanation:

Given that -

$\implies \sf 8 {}^{x - 1} = 2 {}^{x + 3} \\ \\ \implies \sf 2 {}^{3(x - 1)} = 2 {}^{x + 3} \\ \\ \bf we \: can \: observe \: that, \\ \bf bases \: are \: same : \\ \\ \implies \sf 3(x - 1) = x +3 \\ \\ \implies \sf 3x - 3 = x + 3 \\ \\ \implies \sf 3x - x = 3 + 3 \\ \\ \implies \sf 2x = 6 \\ \\ \implies \sf x = \frac{6}{2} \\ \\ \implies \sf x = 3$

Hence, the value of x is 3.

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Verification:

Substituting the value of x in the above equation ;

$\implies \sf 8 {}^{x - 1} = 2 {}^{x + 3} \\ \\ \implies \sf 8 {}^{3 - 1} = 2 {}^{3 + 3} \\ \\ \implies \sf 8 {}^{2} = 2 {}^{6} \\ \\ \implies \sf 64 = 64$

∴ LHS = RHS

Hence, the answer is 3.